Standing waves for quasilinear Schrödinger equations involving double exponential growth

Yony Raúl Santaria Leuyacc

doi:10.3934/math.2023086

Standing waves for quasilinear Schrödinger equations involving double exponential growth

Yony Raúl Santaria Leuyacc

Dynamical systems, differential equations and their applications

Research output: Contribution to journal › Article › peer-review

Abstract

We will focus on the existence of nontrivial, nonnegative solutions to the following quasilinear Schrödinger equation where B₁ denotes the unit ball centered at the origin in R² and g behaves like exp(e^s4) as s tends to infinity, the growth of the nonlinearity is motivated by a Trudinder-Moser inequality version, which admits double exponential growth. The proof involves a change of variable (a dual approach) combined with the mountain pass theorem.

Original language	English
Pages (from-to)	1682-1695
Number of pages	14
Journal	AIMS Mathematics
Volume	8
Issue number	1
DOIs	https://doi.org/10.3934/math.2023086
State	Published - 2023

Bibliographical note

Funding Information:
The author would like to thank the anonymous referees for very careful reading of the manuscript and helpful comments. This work was financed by CONCYTEC-PROCIENCIA within the call for proposal “Proyecto de Investigación Básica 2019-01[Contract Number 410-2019]” .

Publisher Copyright:
© 2023, American Institute of Mathematical Sciences. All rights reserved.

Keywords

Trudinger-Moser inequality
double exponential growth
dual approach
mountain pass theorem
quasilinear Schrödinger equation

Access to Document

10.3934/math.2023086

Cite this

@article{fb02751a43bd46a08d0be9ce0faf34f8,

title = "Standing waves for quasilinear Schr{\"o}dinger equations involving double exponential growth",

abstract = "We will focus on the existence of nontrivial, nonnegative solutions to the following quasilinear Schr{\"o}dinger equation where B1 denotes the unit ball centered at the origin in R2 and g behaves like exp(es4) as s tends to infinity, the growth of the nonlinearity is motivated by a Trudinder-Moser inequality version, which admits double exponential growth. The proof involves a change of variable (a dual approach) combined with the mountain pass theorem.",

keywords = "Trudinger-Moser inequality, double exponential growth, dual approach, mountain pass theorem, quasilinear Schr{\"o}dinger equation",

author = "Leuyacc, {Yony Ra{\'u}l Santaria}",

year = "2023",

doi = "10.3934/math.2023086",

language = "Ingl{\'e}s",

volume = "8",

pages = "1682--1695",

journal = "AIMS Mathematics",

issn = "2473-6988",

publisher = "AIMS Press",

number = "1",

}

TY - JOUR

T1 - Standing waves for quasilinear Schrödinger equations involving double exponential growth

AU - Leuyacc, Yony Raúl Santaria

PY - 2023

Y1 - 2023

N2 - We will focus on the existence of nontrivial, nonnegative solutions to the following quasilinear Schrödinger equation where B1 denotes the unit ball centered at the origin in R2 and g behaves like exp(es4) as s tends to infinity, the growth of the nonlinearity is motivated by a Trudinder-Moser inequality version, which admits double exponential growth. The proof involves a change of variable (a dual approach) combined with the mountain pass theorem.

AB - We will focus on the existence of nontrivial, nonnegative solutions to the following quasilinear Schrödinger equation where B1 denotes the unit ball centered at the origin in R2 and g behaves like exp(es4) as s tends to infinity, the growth of the nonlinearity is motivated by a Trudinder-Moser inequality version, which admits double exponential growth. The proof involves a change of variable (a dual approach) combined with the mountain pass theorem.

KW - Trudinger-Moser inequality

KW - double exponential growth

KW - dual approach

KW - mountain pass theorem

KW - quasilinear Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=85140213980&partnerID=8YFLogxK

U2 - 10.3934/math.2023086

DO - 10.3934/math.2023086

M3 - Artículo

AN - SCOPUS:85140213980

SN - 2473-6988

VL - 8

SP - 1682

EP - 1695

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 1

ER -

Standing waves for quasilinear Schrödinger equations involving double exponential growth

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this